{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ***Introduction to Radar Using Python and MATLAB***\n",
    "## Andy Harrison - Copyright (C) 2019 Artech House\n",
    "<br/>\n",
    "\n",
    "# Probability of Detection with Gaussian Noise\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Referring to Section 6.1.2, to calculate the probability of false alarm for the Gaussian noise and given detection threshold, start with (Equation 6.7) and make use of (Equation 6.1) to give (Equation 6.8)\n",
    "\n",
    "$$\n",
    "    P_{{fa}} = \\int\\limits_{R(\\lambda)} p(y|H_0)\\, dy = \\int\\limits_{V_t}^\\infty  \\frac{1}{\\sigma \\sqrt{2\\pi}}\\, \\exp\\left(-\\dfrac{y^2}{2\\sigma^2}\\right) \\, dy.\n",
    "$$\n",
    "\n",
    "The integral in (Equation 6.8) above may be found in various look-up tables and online calculators, and is given here as (Equation 6.9)\n",
    "\n",
    "$$\n",
    "    P_{{fa}} = \\frac{1}{2}\\left[1 - {erf}\\left( \\frac{V_T}{\\sqrt{2}\\sigma} \\right)\\right],\n",
    "$$\n",
    "\n",
    "where ${erf}$ is the ***error function***.  The error function may be calculated using the SciPy implementation given in ***scipy.special.erf()***. A similar derivation for the probability of detection is followed.  Assume the amplitude of the signal from the envelope detector is $A$, which allows the probability of detection to be written as (Equation 6.10)\n",
    "\n",
    "$$\n",
    "\tP_d = \\int\\limits_{R(\\lambda)} p(y|H1)\\, dy = \\int\\limits_{V_T}^\\infty \\frac{1}{\\sigma \\sqrt{2 \\pi}} \\exp\\left(\\frac{-(y - A)^2}{2\\sigma^2}\\right)\\, dy.\n",
    "$$\n",
    "\n",
    "Performing the integration leads to (Equation 6.11)\n",
    "\n",
    "$$\n",
    "    P_d = \\frac{1}{2}\\left[1 - {erf}\\left( \\frac{V_T - A}{\\sqrt{2}\\sigma} \\right)\\right].\n",
    "$$\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Begin by getting the library path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import lib_path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the start and end signal to noise ratio (dB) and create an array ov values using `linspace` from `scipy`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import linspace\n",
    "\n",
    "snr_start = 1.0\n",
    "\n",
    "snr_end = 20.0\n",
    "\n",
    "snr = 10.0 ** (linspace(snr_start, snr_end, 200) / 10.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the probability of false alarm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "pfa = 1e-6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the probability of detection for gaussian noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from Libs.detection.single_pulse import pd_gaussian\n",
    "\n",
    "pd = pd_gaussian(snr, pfa)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display the probability of detection for gaussian noise using the `matplotlib` routines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from numpy import log10\n",
    "\n",
    "\n",
    "# Set the figure size\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (15, 10)\n",
    "\n",
    "\n",
    "# Display the results\n",
    "\n",
    "plt.plot(10.0 * log10(snr), pd, '')\n",
    "\n",
    "        \n",
    "# Set the plot title and labels\n",
    "\n",
    "plt.title('Pd - Gaussian Noise', size=14)\n",
    "\n",
    "plt.xlabel('Signal to Noise (dB)', size=12)\n",
    "\n",
    "plt.ylabel('Probability of Detection', size=12)\n",
    "        \n",
    "\n",
    "# Set the tick label size\n",
    "plt.tick_params(labelsize=12)\n",
    "        \n",
    "\n",
    "# Turn on the grid\n",
    "plt.grid(linestyle=':', linewidth=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
